Effects of Lorentz boosts on Dirac bispinor entanglement

TL;DR

This paper investigates how Lorentz boosts affect quantum entanglement in Dirac bispinor states, revealing invariance in particle-particle entanglement but degradation in spin-spin entanglement at high velocities, with implications for relativistic quantum information.

Contribution

It provides a detailed analysis of entanglement transformation properties in Dirac bispinors under Lorentz boosts, highlighting differences from previous approaches and clarifying the behavior of various bipartitions.

Findings

Particle-particle entanglement remains invariant under boosts with definite momentum.

Spin-spin entanglement decreases at high boost velocities.

Differences between bispinor approach and traditional spin-momentum entanglement are discussed.

Abstract

In this paper we describe the transformation properties of quantum entanglement encoded in a pair of spin 1/2 particles described via Dirac bispinors. Due to the intrinsic parity-spin internal structure of the bispinors, the joint state is a four-qubit state exhibiting multipartite entanglement, and to compute global correlation properties we consider the averaged negativities over each possible bi-partition. We also consider specific bipartitions, such as the spin-spin and the particle-particle bipartitions. The particle-particle entanglement, between all degrees of freedom of one particle and all degrees of freedom of the other particle, is invariant under boosts if each particle has a definite momentum, although the spin-spin entanglement is degraded for high speed boosts. Correspondingly, the mean negativities are not invariant since the boost drives changes into correlations encoded in specific bipartitions. Finally, the results presented in the literature about spin-momentum entanglement are recovered by considering the projection of bispinorial states into positive intrinsic parity, and some striking differences between the appropriate approach for this case and the one usually treated in the literature are discussed.